Simple Function

A simple function is a finite sum sum_(i)a_ichi_(A_i), where the functions chi_(A_i) are characteristic functions on a set A. Another description of a simple function is a function that takes on finitely many values in its range.

The collection of simple functions is closed under addition and multiplication. In addition, it is easy to integrate a simple function. By approximating a given function f by simple functions, the Lebesgue integral of f can be calculated.

See also

Characteristic Function, Lebesgue Integrable, Lebesgue Integral, Set

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "Simple Function." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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